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Maybe-svexlist-rewrite-fixpoint

Signature

(maybe-svexlist-rewrite-fixpoint x do-it) → new-x

Arguments

x — Guard (svexlist-p x).

Returns

new-x — Type (svexlist-p new-x).

Definitions and Theorems

Function: maybe-svexlist-rewrite-fixpoint

(defun maybe-svexlist-rewrite-fixpoint (x do-it)
  (declare (xargs :guard (svexlist-p x)))
  (let ((__function__ 'maybe-svexlist-rewrite-fixpoint))
    (declare (ignorable __function__))
    (if do-it (svexlist-rewrite-fixpoint-memo x)
      (hons-copy (svexlist-fix x)))))

Theorem: svexlist-p-of-maybe-svexlist-rewrite-fixpoint

(defthm svexlist-p-of-maybe-svexlist-rewrite-fixpoint
  (b* ((new-x (maybe-svexlist-rewrite-fixpoint x do-it)))
    (svexlist-p new-x))
  :rule-classes :rewrite)

Theorem: maybe-svexlist-rewrite-fixpoint-correct

(defthm maybe-svexlist-rewrite-fixpoint-correct
  (b* ((?new-x (maybe-svexlist-rewrite-fixpoint x do-it)))
    (equal (svexlist-eval new-x env)
           (svexlist-eval x env))))

Theorem: maybe-svexlist-rewrite-fixpoint-len

(defthm maybe-svexlist-rewrite-fixpoint-len
  (b* ((?new-x (maybe-svexlist-rewrite-fixpoint x do-it)))
    (equal (len new-x) (len x))))

Theorem: vars-of-maybe-svexlist-rewrite-fixpoint

(defthm vars-of-maybe-svexlist-rewrite-fixpoint
  (b* ((?new-x (maybe-svexlist-rewrite-fixpoint x do-it)))
    (implies (not (member v (svexlist-vars x)))
             (not (member v (svexlist-vars new-x))))))

Theorem: maybe-svexlist-rewrite-fixpoint-of-svexlist-fix-x

(defthm maybe-svexlist-rewrite-fixpoint-of-svexlist-fix-x
  (equal (maybe-svexlist-rewrite-fixpoint (svexlist-fix x)
                                          do-it)
         (maybe-svexlist-rewrite-fixpoint x do-it)))

Theorem: maybe-svexlist-rewrite-fixpoint-svexlist-equiv-congruence-on-x

(defthm
     maybe-svexlist-rewrite-fixpoint-svexlist-equiv-congruence-on-x
  (implies (svexlist-equiv x x-equiv)
           (equal (maybe-svexlist-rewrite-fixpoint x do-it)
                  (maybe-svexlist-rewrite-fixpoint x-equiv do-it)))
  :rule-classes :congruence)